Combining weight, balance and swingweight

The two racquets have the same swingweight when measured in the plane normal to the stringbed, but if you mounted them in an RDC machine with the handle rotated 90 degrees to measure the swingweight in the plane of the stringbed, the racquet with higher twistweight would measure higher swingweight than the other because the added weight on the sides of the hoop is farther from the pivot point than if the weight were placed in the center of the stringbed.

Your actual swing occurs in a plane that is neither completely normal nor completely parallel to the stringbed, so the twistweight contributes to the "effective" swingweight, which is always slightly higher than the measured swingweight. In most cases, the difference between measured swingweight and "effective" swingweight is consistent enough that it is not worth worrying about the difference. But the example presented (with 2 frames of equal mass, balance, and measured SW, but different mass distributions) is a case where the difference does come into play.

I have to go catch a plane this morning, so I'll leave a drawing to someone else.

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sure, I get all of that. But you never said before that 'I' in your MgR/I equation is (as you call it) 'effective swingweight'. And if it is - than aren't all your line of thinking based on observed correlation between ATP player's racket specs and MgR/I of those rackets kind of baseless? Since I'm pretty sure that all data about player's rackets refers to what commonly is known as 'swingweight' and not 'effective swingweight'?
Also, isn't saying "In most cases, the difference between measured swingweight and "effective" swingweight is consistent enough that it is not worth worrying about the difference." a bit misleading? As you pointed out yourself - if you add weight to the sides of the racket the 'effective swingweight' actually changes apparently noticeably. Isn't adding weight to the sides of the racket like at least as common as adding the weight at the top or bottom of the racket? In other words 'most cases' is like 50% of the cases, no?

The two racquets have the same swingweight when measured in the plane normal to the stringbed, but if you mounted them in an RDC machine with the handle rotated 90 degrees to measure the swingweight in the plane of the stringbed, the racquet with higher twistweight would measure higher swingweight than the other because the added weight on the sides of the hoop is farther from the pivot point than if the weight were placed in the center of the stringbed.

Your actual swing occurs in a plane that is neither completely normal nor completely parallel to the stringbed, so the twistweight contributes to the "effective" swingweight, which is always slightly higher than the measured swingweight. In most cases, the difference between measured swingweight and "effective" swingweight is consistent enough that it is not worth worrying about the difference. But the example presented (with 2 frames of equal mass, balance, and measured SW, but different mass distributions) is a case where the difference does come into play.

I have to go catch a plane this morning, so I'll leave a drawing to someone else.

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Some corrections and clarifications: The swing weight (Ix) is measured around an axis in the plane of the string bed (x-axis), not normal to it (but you probably mean that).

The twist weight (Iy) is measured around an axis along the length of the racquet (y-axis) and affects the swing very little (but is important at an off-line impact).

It is right that a normal swing not is entirely around the string bed plane and that the actual swingweight is a little higher. The moment of inertia (Iz) around the third axis is higher than the swingweight, which follows from perpendicular axis theorem Iz=Ix+Iy. However, in a racquet these two "swingweights" (Ix and Iz) are similar since Iy is small, so their combined effect from not swinging entirely around the x-axis is fairly small.

An example: assume an evenly balanced racquet with a weight of 320 g, a swing weight (Ix) of 325 kg cm^2 and a twist weight (Iy) of 15 kg cm^2 ( a typical value). Using the the parallel axis and perpendicular axis theorems you get that Iz is 340 kg cm^2 . That is the swingweight if you swing with edge towards the ball (not so common). If you swing with racquet with the head tilted at some other angle it is much more complicated and you have to involve the products inertia as well. But assuming that the racquet is flat ( a fair assumption) you approximate the moment of inertia at an angle a with Ia = Ix*(cos a)^2+ Iz*(sin a)^2 if a is 45 degrees Ia becomes the average of the two. So the swingweight of a swing with the head at 45 degree angle is 332 or 2% higher. More importantly, this increase is almost the same for all racquets, so it is hardly worth bothering about.

Tonight I played with 2 identical rackets and customized to same endspecs, 327 g, 33.3 balance, 335 sw.

One racket had all the added weight at the sides and the other one in a more polarized manner.

The played very different despite having the same curve (and the same MgR/I). I am not only referring to ball trajectory, but also the felt racketheadcontrol. The polarized one has a whippier feel than the other one.

The equivalent mass is the same for both rackets, but do you know why they play so different? I think I know why just by experience, but it would be great if there was a scientific explanation.

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travlerajm is correct that they have a different twist weight (moment of inertia around the y-axis). As I discussed above that doesn't influence the speed of the swing that much (and thus not the curve). However, it does influence the feel of the racquet, especially at impact. Placing weights at 3 and 9 increases the twist weight whereas placing it at 12 doesn't. A racquet with high twist weight feels less "wobbly" i.e. it is more difficult to rotate around its length axis. It can also handle an off line hit a little better (if you ever miss the sweet spot) and transfers a little less twist to the arm.

Some corrections and clarifications: The swing weight (Ix) is measured around an axis in the plane of the string bed (x-axis), not normal to it (but you probably mean that).

The twist weight (Iy) is measured around an axis along the length of the racquet (y-axis) and affects the swing very little (but is important at an off-line impact).

It is right that a normal swing not is entirely around the string bed plane and that the actual swingweight is a little higher. The moment of inertia (Iz) around the third axis is higher than the swingweight, which follows from perpendicular axis theorem Iz=Ix+Iy. However, in a racquet these two "swingweights" (Ix and Iz) are similar since Iy is small, so their combined effect from not swinging entirely around the x-axis is fairly small.

An example: assume an evenly balanced racquet with a weight of 320 g, a swing weight (Ix) of 325 kg cm^2 and a twist weight (Iy) of 15 kg cm^2 ( a typical value). Using the the parallel axis and perpendicular axis theorems you get that Iz is 340 kg cm^2 . That is the swingweight if you swing with edge towards the ball (not so common). If you swing with racquet with the head tilted at some other angle it is much more complicated and you have to involve the products inertia as well. But assuming that the racquet is flat ( a fair assumption) you approximate the moment of inertia at an angle a with Ia = Ix*(cos a)^2+ Iz*(sin a)^2 if a is 45 degrees Ia becomes the average of the two. So the swingweight of a swing with the head at 45 degree angle is 332 or 2% higher. More importantly, this increase is almost the same for all racquets, so it is hardly worth bothering about.

travlerajm is correct that they have a different twist weight (moment of inertia around the y-axis). As I discussed above that doesn't influence the speed of the swing that much (and thus not the curve). However, it does influence the feel of the racquet, especially at impact. Placing weights at 3 and 9 increases the twist weight whereas placing it at 12 doesn't. A racquet with high twist weight feels less "wobbly" i.e. it is more difficult to rotate around its length axis. It can also handle an off line hit a little better (if you ever miss the sweet spot) and transfers a little less twist to the arm.

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@stoneage - yes, this is excellent explanation, and more importantly based on physics and not 'feel'. I never had any doubts you understand the nuances. I get all of that.
But what I do not understand is whether in MgR/I equation one shall use:
a) Ix (which is what is being published as 'swingweight')? or
b) Ix + Iz (which would take into account twistweight as well)?

Because in all previous threads and posts the only value ever mentioned or discussed was Ix.
Now, when JohnB points out that two rackets with identical mass, balance, and swingweight (Ix) - which obviously means that MgR/I is also identical - do feel differently, travlerajm says that this is expected since the twistweight (Iy) of those two rackets is different.
well, which is it than? Either 'I' in MgR/I is just Ix and you at least can claim you are using published specs to back up your claims. Or 'I' in MgR/I is 'Ix+Iy' and than the entire line of thinking backing up this MgR/I idea needs to be redone since:
- no one measures Ix+Iy unless specifically told to do so, and
- therefore people were tuning rackets to MgR/I=21.0 using incorrect value of I, and
- there's no way to compare that to pro's racket specs since they do not publish Iy of pros rackets.

@stoneage - yes, this is excellent explanation, and more importantly based on physics and not 'feel'. I never had any doubts you understand the nuances. I get all of that.
But what I do not understand is whether in MgR/I equation one shall use:
a) Ix (which is what is being published as 'swingweight')? or
b) Ix + Iz (which would take into account twistweight as well)?

Because in all previous threads and posts the only value ever mentioned or discussed was Ix.
Now, when JohnB points out that two rackets with identical mass, balance, and swingweight (Ix) - which obviously means that MgR/I is also identical - do feel differently, travlerajm says that this is expected since the twistweight (Iy) of those two rackets is different.
well, which is it than? Either 'I' in MgR/I is just Ix and you at least can claim you are using published specs to back up your claims. Or 'I' in MgR/I is 'Ix+Iy' and than the entire line of thinking backing up this MgR/I idea needs to be redone since:
- no one measures Ix+Iy unless specifically told to do so, and
- therefore people were tuning rackets to MgR/I=21.0 using incorrect value of I, and
- there's no way to compare that to pro's racket specs since they do not publish Iy of pros rackets.

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To elaborate a little more on my previous answer and my view on this:
The twist weight is Iy, i.e. around the y-axis. The swing occurs mainly around the x and z axis, and is "controlled" by a combination of Ix and Iz, but since they are fairly similar the error by using only Ix, i.e. the swingweight, is small. So my first conclusion is: you can continue to use swingweight as before.

The twistweight will affect the feel of the racquet, but it doesn't influence the swing that much and can therefore be treated as a separate problem. Still I think twistweight is a neglected parameter that is worth keeping an eye on. Some more about twist weight here:

I am not going to comment on what to use in MgR/I since I don't know (I have yet to see a reasonable explanation how MgR/I influence a tennis swing).

@stoneage Thanks for your many technical posts. This is an interesting attempt to develop a new way of looking at the weight parameters of racquets.

However, I believe there is a mistake in the formula in your effective_mass.xlsx spreadsheet. There is an extra factor of 2 in the denominator there. When you take that out, the plots become monotonic with 15/r and you get much larger effective masses on the right side.

In the eqv_mass_norm.xlsx spreadsheet, I don't understand the expression for the reference racquet that you use in the denominator there. Can you explain how Ip for the reference racquet equals 320 (1033 + 50*r + r*r) ?

Using I[end] = (M*L^2)/3 for a uniform rod, I get
Ip = 320 (70*70/3 + r*r) for the reference racquet. This makes the curves look quite different.

Anyways, thanks for posting something that was motivating enough to get me to finally de-lurk!

@stoneage Thanks for your many technical posts. This is an interesting attempt to develop a new way of looking at the weight parameters of racquets.

However, I believe there is a mistake in the formula in your effective_mass.xlsx spreadsheet. There is an extra factor of 2 in the denominator there. When you take that out, the plots become monotonic with 15/r and you get much larger effective masses on the right side.

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I hate to admit it, but you are absolutely right! The 2 shouldn't be there. I have updated the Excel sheet. The change alters the curves as you have noticed. I don't think that there is a much difference in the relation between the racquets, but since the curve rises faster it is more difficult to see the difference. It is therefore even more motivated to use the normalized diagram instead (which never had the irritating 2). Thanks a lot for pointing it out even if it was embarrassing

In the eqv_mass_norm.xlsx spreadsheet, I don't understand the expression for the reference racquet that you use in the denominator there. Can you explain how Ip for the reference racquet equals 320 (1033 + 50*r + r*r) ?

Using I[end] = (M*L^2)/3 for a uniform rod, I get
Ip = 320 (70*70/3 + r*r) for the reference racquet. This makes the curves look quite different.

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Not quite. r is defined as the distance to the point 10 cm up the handle where the force is applied. So starting with the MOI around the midpoint, Ip for the rod is:
Ip=M*L^2/12+M*(c+r)^2

and c for an evenly balanced rod is L/2-10 = 25 so I get
Ip=M*70*70/12+M*(25+r)^2= M*(1033+50*r+r*r)

Also remember that the parallel axis theorem can only be used in relation to the MOI around the center of mass, so you can't calculate Ip the way you did, even if r would have been to the endpoint of the racquet.

When matching racket/weights to players, there is NO direct corelation between a certain fix and the player's ability to PLAY better. Too many X factors come to play.

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There certainly are! The purpose of the curve is to visualize some important parameters and hopefully make it easier so see the difference between racquets. It is not a prescription how to optimize a racquet.

The level of tennis you can achieve is only to a small degree determined by the balance of your racquet (Federer would beat me with an iron spade). But getting a racquet that feels fine will make it more fun och you will probably play better. The placebo effect is at least as important as the physics.

@stoneage Thanks for your response explaining the correct Ip for the uniform reference racquet. My mangling of the parallel axis theorem and inability to figure out your correct expression might be more embarrassing than your extra factor of 2! I'll get over it someday.

Now that (hopefully) the math is checked out, we can talk about the interpretation of the model and its results. The "effective mass" was an interesting idea, but I wasn't comfortable with the mixing of linear and angular forces. I didn't know what to make of effective masses of 500 (or 700) grams at small values of r. So the "mass" numbers were no more intuitive than swingweights.

The normalization was an improvement, certainly, but since it's now dimensionless quantity, there's no concept of "mass" anymore. And since me/me0 = Ip/Ip0, you only need starting equations 5 and 6 in your proof. Equations 1-4 aren't needed, and we're just plotting the ratios of moments vs. radius of swing.

Still, this is pretty cool. You can plot the moments of two racquets and say something like Racquet A takes 21% less effort to swing on serves than Racquet B, and 11% less effort on forehands. Just need to pick values of r that represent the serve and the forehand. (Let's ignore the fact that the serve is a complex motion involving multiple radii at different phases.) I think that would be about as readily understandable as you can get. And it's a big improvement over just taking the ratios of the conventional swingweights. Your fundamental insight is that 10cm from the butt is the wrong axis of rotation to care about, and looking at longer radii shows that swingweight numbers understate the differences in swing effort.

After we revolutionize the reporting of swingweight, we can tackle the endless argument whether racquet speed or weight is more important when the racquet hits a tennis ball.

The level of tennis you can achieve is only to a small degree determined by the balance of your racquet (Federer would beat me with an iron spade). But getting a racquet that feels fine will make it more fun och you will probably play better. The placebo effect is at least as important as the physics.

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I see this so often on this boards that I just can't believe people that read Tennis Talk (which means they have more than average knowledge and interest in tennis) are able to overlook this important field!

No doubt a perfectly tuned racket wouldn't make you win against Federer, nor even against your best club player!

But it will give you some leverage that's for sure.
If it will improve your game for only 5-10% - great! I would take any factor that would improve my game by that much and put me slightly ahead in fron of my competition at 4.0 level!

There certainly are! The purpose of the curve is to visualize some important parameters and hopefully make it easier so see the difference between racquets. It is not a prescription how to optimize a racquet.

The level of tennis you can achieve is only to a small degree determined by the balance of your racquet (Federer would beat me with an iron spade). But getting a racquet that feels fine will make it more fun och you will probably play better. The placebo effect is at least as important as the physics.

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It looks like, from your graphs, that adding weight in a non-polarized manner makes it harder for you to achieve the same end result (swinging the racquet along any axis from your body) than adding it in a polarized manner.

Say I want a SW of 350. I do this by adding 8g in the hoop and 8g in the butt. My balance remains the same, and my curve on your graph will be parallel between the unmodified racquet and the modified racquet. This means that I have access to this added mass in a predictable and linear manner, as it's deviation from the mean is equal across all data points.

If I want the same SW of 350 but I do it by adding 5 g in the hoop and nowhere else, then its a de-polarized customization and my balance is thrown off... its more or less head heavy now. My access to the added mass increases exponentially away from the mean the further my axis point travels from the core of my body. This means that depending on where my axis is, it will be harder to swing the racquet by a factor that is exponentially larger than any point prior to that axis. I think that can confuse the mind-body mechanics and negatively affect timing.

IMO, a depolarized setup gets you to a point of diminishing returns quicker because the added mass you may want will not equal what you need depending on where the axis is. It certainly does for a while, but if for some reason you're stretched out far trying to make a stab volley and the axis is at your wrist, a depolarized racquet will actually make it harder for you to access that added mass -- and may even hurt you -- due to the fact that it requires so much more effort on your part than it did when you were swinging from your shoulder.

@stoneage Thanks for your response explaining the correct Ip for the uniform reference racquet. My mangling of the parallel axis theorem and inability to figure out your correct expression might be more embarrassing than your extra factor of 2! I'll get over it someday.

Now that (hopefully) the math is checked out, we can talk about the interpretation of the model and its results. The "effective mass" was an interesting idea, but I wasn't comfortable with the mixing of linear and angular forces. I didn't know what to make of effective masses of 500 (or 700) grams at small values of r. So the "mass" numbers were no more intuitive than swingweights.

The normalization was an improvement, certainly, but since it's now dimensionless quantity, there's no concept of "mass" anymore. And since me/me0 = Ip/Ip0, you only need starting equations 5 and 6 in your proof. Equations 1-4 aren't needed, and we're just plotting the ratios of moments vs. radius of swing. This curve loses a part for the very long swing radii, but instead shows the part where you go from r=0 where meausure swing to just outside the handle

Still, this is pretty cool. You can plot the moments of two racquets and say something like Racquet A takes 21% less effort to swing on serves than Racquet B, and 11% less effort on forehands. Just need to pick values of r that represent the serve and the forehand. (Let's ignore the fact that the serve is a complex motion involving multiple radii at different phases.) I think that would be about as readily understandable as you can get. And it's a big improvement over just taking the ratios of the conventional swingweights. Your fundamental insight is that 10cm from the butt is the wrong axis of rotation to care about, and looking at longer radii shows that swingweight numbers understate the differences in swing effort.

After we revolutionize the reporting of swingweight, we can tackle the endless argument whether racquet speed or weight is more important when the racquet hits a tennis ball.

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Great input, you are right about a lot of things here. The original equation is very simple and contains some unspoken simplification (like assuming that the racquet is attached to a massless rod). I also agree that the effective mass becomes a little hard to understand for short swing radii. However, I still thought it was useful since my aim was to compare racquets, not to give absolute values. Normalizing made the difference more clear, but I am aware that, as you point out, I am really leaving the equivalent mass idea. I still kept it since I started talking about equivalent mass. But you are probably right that it is better to just talk about relative swing weight.

If I keep the reference racquet as before an plot a curve of Ip/Ipref it will look the same as the Me/Meref (not surprise).

The advantage is that we longer need the equations as background. While we are at it we might as well plot it against the the swing radius r instead of 15/r since it is easier to understand. The reason for using 15/r was that Me had no relevance for r=0, whereas MOI has. So instead we get a figure like this:

It shows the same relation as the first figure, but with short swings to the left instead of to the right. The advantage is that you can see the actual values of the swing radius, which is more intuitive. This curve looses a part for very long radii (probably not so interesting). But instead shows the difference between r=0, where you measure swing weight and the wrist at r=15.

It looks like, from your graphs, that adding weight in a non-polarized manner makes it harder for you to achieve the same end result (swinging the racquet along any axis from your body) than adding it in a polarized manner.

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I would say the opposite. A "polarized" racquet has a higher swing weight than a non polarized with the same weight and balance. Increasing the swing weight more than the weight will push up one of the curve.

If add a weight around 42 cm from the but end, shape of the curve will remain pretty much the same, it will just be pushed upwards.

Yes, plotting r instead of 15/r is much better. An alternative option for plotting is to plot the ratio of the racquet moments to each other, avoiding the need for a reference broomstick--although I like the idea of an official reference broomstick, maybe gold-plated and enshrined somewhere.

An example of the swingweight-ratio-of-two-racquets plot:

In this plot it's easy to see the Pro Staff has roughly equal swingweight at the wrist, roughly 8-10% more at the elbow, roughly 13-14% more at the shoulder. That's why your arm will fatigue faster with that racquet, even though it's the "lower" swingweight racquet at the traditional reference axis.

I really like the results of this thread, even if all we have done is a) think about a realistic axis of rotation, and b) use the parallel axis theorem.

This is significant because the traditionally-defined swingweight axis clearly doesn't give us the best number to predict arm fatigue, or even indicate how easy or hard it feels to swing a forehand! If it ever worked for such purposes, it was a coincidence owing to racquets under comparison being very close in mass distribution. If I had to pick a single replacement without further study, I'd choose swingweight at the elbow radius, say r=40. That radius applies to arm-stressing portions of the groundstrokes and the middle phase of the serve. And "tennis elbow" is the epidemic, not "tennis wrist" or "tennis shoulder" although those are bad too.

Maybe the traditional axis was intended to be more relevant to the effects of ball-impact, since it represents the axis where torque is applied to resist the ball, but those dynamics depend more specifically on mass distribution than the static swingweight number can capture. We're lucky that TWU is now full of better measurements--power potential, plowthrough, etc.--which quantify and summarize impact effects.

What I'd like to see developed is the most realistic number for predicting arm fatigue, so if I had that number, and I knew what my limit was, I'd know whether the racquet was too heavy or not. This thread shows the significance of swingweight on a more realistic axis of rotation, which is the torque required for a given angular acceleration. Right now, I'd use the swingweight at r=40 (or maybe an average of the swingweights at r=15, 40, and 60) as my magic number for "racquet heaviness."

For me, the next theoretical step would be to consider the maximum centrifugal force caused by the racquet, which would occur at the point of contact of a serve, and try to figure out if that tells me anything different about racquet heaviness. If the racquet speed is high enough, I wonder if centrifugal force outweights torque as a cause of arm fatigue.

Yes, plotting r instead of 15/r is much better. An alternative option for plotting is to plot the ratio of the racquet moments to each other, avoiding the need for a reference broomstick--although I like the idea of an official reference broomstick, maybe gold-plated and enshrined somewhere.

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OK, then plotting against r is decided by the International Relative Swing Weight Comity (IRSWC).

Plotting the two racquets against each other is really useful when you want to compare them and make them similar. And you don't have to deal with the somewhat arbitrary reference stick. However, if you have more than two racquets it can be confusing. You also miss the information whether they are heavier for shorter or longer swings, i.e. both can have a descending curve without it being visible. So I think that both ways to plot have their merit and can be used in parallel.

I have therefore made a new excel sheet with both curves that you can download here.

Namely, first I will up the swingweight enough of the polarized racket to match it to the effective swingweight of the higher twistweight racket and then compare.

Second I will try to set-up both rackets, one more polarized than the other, but now not only with identical mass, balance and swingweight, but also with the same twistweight and then compare.

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Having done so, here are my findings.

When I matched the polarized racket's swingweight to the effective swingweight of the high twistweight racket while keeping balance and mass equal, they felt pretty much the same. The polarized one felt slightly whippier, but I had just about the same control over the rackethead.

When I matched balance, swingweight, static weight and twistweight I couldn't tell them apart swingwise. The only difference was during impact. The polarized one had a longer dwelltime.

MgR/I uses swingweight as part of it's formula. Should swingweight be replaced with relative swingweight in the MgR/I formula?

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No, you should not, since relative swing weight is not one value but a curve. You could of course play with it by putting in relative swing weight and vary R the same amount. But I have no idea what that would say (on the other hand, I don't understand what MgR/I is supposed to say to begin with).

Thanks. Hopefully you and travlerajm can get together and work on mgr/i.

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Sorry, but that is not going to happen.
I have tried both to get some useful information about what mgr/i is supposed to mean and to contribute, but the response has been discouraging to say the least.

Do you think relative swingweight should replace swingweight in racket specs and RDC machines?

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No. Moment of inertia (swingweight) is, together with balance and weight, one of the fundamental parameters that describe the behavior of the racquet. And you need that to create the relative swingweight curve.

My aim with the curve was to increase the understanding of how these three parameters affect the racquet for different swings.

The result of the plot seems to be quite well matched with my experience...the curves are similar in shape, and converge towards the "around wrist" value.
I take it that means that on short swings there's not much difference but on longer swings the difference grows.
If my understanding is correct, that matches pretty well with my subjective experience of the differences...there's not much difference in maneuverability on volleys, but I feel the new spec more snappy on serves and forehands...and as a result it tires me out slightly less late in the 3rd set.

This is a very interesting thread about an item that we (of the Dutch forum) also worked on.
We noticed that too many children play with a racquet that is either too heavy or too light for their age, type of play or stature.

So we created the Swingweight advisor which does the following:
This Excel sheet does 3 things:
1. It advises a Swingweight for a certain player based on type of forehand, age and build.
2. It calculates the SW of a racquet, when head- and throat- weight are entered. (Only have to weigh the weight at both ends of the racquet)
3. When the SW is too low it calculates how much weight should be added at a certain position.

There has been a lot of discussions about this on different forums and people built weighing systems to measure the SW as shown on this pictures.

Only one scale is ok but we found out that Head does the same measurements with 2 scales which is easier of course.

Maybe this is useful to you and when someone wants to have the Excelsheet just send me a pm.

[...]
2. It calculates the SW of a racquet, when head- and throat- weight are entered. (Only have to weigh the weight at both ends of the racquet)
3. When the SW is too low it calculates how much weight should be added at a certain position.

There has been a lot of discussions about this on different forums and people built weighing systems to measure the SW as shown on this pictures.

Only one scale is ok but we found out that Head does the same measurements with 2 scales which is easier of course.

[..]

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this method does not measure the swingweight. It measures the balance. You can than use the measured balance, weight, and the length to --approximate-- the swingweight. Depending on how the weight is distributed on a given racket the swingweight approximation will vary (sometimes it will be fairly accurate, sometimes not so much. For non-customized rackets it will be likely pretty good approximation).
But to be technically exact you cannot measure the swingweight that way

The calculation goes as follows:
- From the head and throat weight the balance point is calculated.
- Then the moment of enertia is calculated from the balance point.
- Then the moment of enertia of is added for the displacement from the balance point to the rotation point that you want to choose. This rotation point lies on 10 cm from the end of the grip on most of the SW machines.

We compared the calculated values (Schwunggewicht berechnet) with the values measured on an Babolat RDC (Schwunggewicht gemessen) and as you can see these are quite close.

If you take into consideration that SW’s measured on different machines differ a lot these values do not differ too much.

The calculation goes as follows:
- From the head and throat weight the balance point is calculated.
- Then the moment of enertia is calculated from the balance point.
- Then the moment of enertia of is added for the displacement from the balance point to the rotation point that you want to choose. This rotation point lies on 10 cm from the end of the grip on most of the SW machines.

We compared the calculated values (Schwunggewicht berechnet) with the values measured on an Babolat RDC (Schwunggewicht gemessen) and as you can see these are quite close.

If you take into consideration that SW’s measured on different machines differ a lot these values do not differ too much.

Bp = distance balance point to end of the grip. (cm)
W = weight (gram)
Tot weight = W head + W throat (gram)
Oset = the offset of the pivot point
1,5 = the approximate radius of the cross section of the racquet (=relatively unimportant).

You can't calculate swing weight/moment of inertia from weight and balance (as JMNK already pointed out). The formula you give might be used to approximate the swing weight for some racquets. But it assumes a certain weight distribution in the racquet so you can never know whether it is correct or not. And in contrast to the real swing weight it doesn't add any new information about the mechanical properties of the racquet.

To give an example why this doesn't work lets consider three racquets, all 70 cm long and with a mass of 250 gram evenly distributed. Then:
to A: Add 50 g evenly distributed
to B: Add 50 g to the midpoint
to C: Add 25 g each to the top and bottom

You end up with three racquets that have that same mass (300 g) and the same balance point. So if you try to calculate the swing weight from these two values you will end up with the same swing weight, independent of which formula you use. With your method all three will be identical.

I might be that your browser is set up to handle xlsx files in some specific way (i.e. not download them).

You might also try change the extension of the downloaded file to xlsx instead of whatever the browser has changed it to.

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Strange, when I open your link I get WinZip opens a zip file called eqv_mass_norm.zip, which contains three folders: _rels, docProps and xl, and a file called [Content_Types].xml. These folders contain a number of mainly .xml docs, but no .xlsx files which I regularly use for my work. In xl, there is a file called workbook.xml that sounds like it could actually be an Excel file.

To give an example why this doesn't work lets consider three racquets, all 70 cm long and with a mass of 250 gram evenly distributed. Then:
to A: Add 50 g evenly distributed
to B: Add 50 g to the midpoint
to C: Add 25 g each to the top and bottom

You end up with three racquets that have that same mass (300 g) and the same balance point. So if you try to calculate the swing weight from these two values you will end up with the same swing weight, independent of which formula you use. With your method all three will be identical.

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I misunderstood the matter at first:
If you add weights in one point you havd to add the Moment of inertia of that weight separately to get the right total SW.

meaning:
In case of adding 25 gram at both ends: a
The added SW with pivot point at 10 cm= 25*(10^2 + (Length - 10)^2 gr >>> 25 * Length^2
In case of the 50 gram in the center
The added SW = 50 * (bal-10)^2

If the balance point is at 35 cm and the length is 70 cm the added SW's are 90 and 31250 kgcm^2.
So this is the same difference as you mention between 350 and 290 kg cm

This is what the last section of the SW advisor calculates when you add weight.

We are testing this system and comparing it with actual SW tests on for quite some time now and we think that it is quite accurate.

Hi Technatic - What is that 8 sided racquet? Is from late 80's? Any info would be appreciated! Thanks - Jack

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It was a sample from a manufacturer, more than 20 years old, I don't think that it was ever produced.

The system certainly calculates different Swingweights for these different cases.

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It certainly does not since the W head and W throat in your formula are the same for all three cases! (You can try it)

The "innovation" of calculating swingweight from balance and weight appears on Talk Tennis at least once a year, so you are not alone in this misconception. The problem is that it works as long as the weight is evenly distributed over racquet, but you can never tell when it doesn't. It also makes the concept of swingweight meaningless since it just a rearrangement of weight and balance. If you don't want to measure swingweight (which is not that difficult) it is better just to talk about weight and balance as such.

Finally, if you look at the definitions of swingweight (J) and balance (R) for and object of length L and weight M:

You can see that both depend on the distribution of mass m(x). But since the integrals are different, you can never use R to calculate J without knowing m(x).
(I have used the one dimensional case to simplify)

I have a little problem off topics but didn't found a thread: Because there wouldn't be an android version in the near future, I got my hand on an Ipod touch 2G with ios firmware 4.2.1. I bought your racquettune app via itunes-appstore. But when I try to install the app, I get the message, that the app isn't compatiblle with my ipod touch. I then saw, that the newest version 4.2.1 of your app requires ios 4.3 or later, which doesn't seem to exit for the touch 2g MC-model. As I noticed, the version 4.1 was made for ios 4.1 or later, which would fit. So where can I "downgrade" from raquettune 4.2.1 to 4.1? Or is there another way to get the 4.2.1. version on an ipod touch 2g?

It certainly does not since the W head and W throat in your formula are the same for all three cases! (You can try it)

The "innovation" of calculating swingweight from balance and weight appears on Talk Tennis at least once a year, so you are not alone in this misconception. The problem is that it works as long as the weight is evenly distributed over racquet, but you can never tell when it doesn't. It also makes the concept of swingweight meaningless since it just a rearrangement of weight and balance. If you don't want to measure swingweight (which is not that difficult) it is better just to talk about weight and balance as such.

Finally, if you look at the definitions of swingweight (J) and balance (R) for and object of length L and weight M:

You can see that both depend on the distribution of mass m(x). But since the integrals are different, you can never use R to calculate J without knowing m(x).
(I have used the one dimensional case to simplify)

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completely agree.

for those that are physics/math challenged Imagine you --could-- in fact accurately and absolutely calculate the swingweight by measuring just the weight, the balance, and the length of an object (or in this case a racket).
Why would Babolat or Prince tuning machines have a special function for measuring a swingweight? Why wouldn't they just measure the weight, the balance, and the length of an object and immediately give you an accurate swingweight value based on some match formula? Or why would Stoneage develop his excellent swingweight measuring app that does require a bit more involved procedure than just weighting a racket ?

Hi guys,
I think that it might be good to discuss our basic intention:

* I certainly understand that people with knowledge about physics will say that it is impossible to calculate the Swingweight of a racquet very accurately.

But the major question is: Do we want a system that makes it possible to compare racquets or do we need very accurate values of the SW?

If we want to compare racquets we need a “measuring system” , with an accuracy that is as high as possible.

Another fact is that test results from different SW machines differ quite a lot, which proves that this is not an easy measurement to do.
So these machines are impressive and expensive but not accurate.

So if there is a much cheaper way to do a test, with about the same accuracy, there is a good reason to choose this test method. And a scale or even 2 scales are much cheaper than one SW machine.

What is our intentions with the SW advisor?
The idea of the SW came up because we advise the Dutch Tennis Ass about material for young children.
- It should avoid that players play with completely the wrong SW and especially young children.
- We want to make it very easy for coaches to advise the right frame for a certain player.

The system does 3 things:
1. It advises a Swingweight for a certain player based on type of forehand, age and build.
2. It calculates the SW of a racquet, when head- and throat- weight are entered. (Only have to weigh the weight at both ends of the racquet)
3. When the SW is too low it calculates how much weight should be added at a certain position to get the desired SW.

So for our purpose we need an advise system, a measuring (calculating system) and a way to customize racquets. This is what the Excel sheet (and the online version later) does.

And of course we wanted to know how accurate our “measuring” system is compared to the official machines.

Our conclusion out of these tests is that the difference between our system and official machines is not bigger than the difference between the different SW machines.

So the inaccuracy of our system is not worse than that of the official machines. And a difference of less than 5% of the measured value is not bad at all for a complicated test.

You will understand that we are not interested in theoretical solutions without practical possibilities.

Why would Babolat or Prince tuning machines have a special function for measuring a swingweight? Why wouldn't they just measure the weight, the balance, and the length of an object and immediately give you an accurate swingweight value based on some match formula?

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There are different reasons for this:
* A swing weight test based on measuring the swing time of an object is a very logic choice. The SW can be calculated with one formula from the swing time
T = 6,28 *rt (SW/w*L)
* Calculating from the Head and throat weight is much more complicated.
* Prince and Babolat sell these machines so it generates income.
* Prince and Babolat may do it with their machine Head seems to do it with the weighing system: http://www.youtube.com/watch?feature=player_embedded&v=lW5huxsH1-Y&noredirect=1

I would like to explain the thoughts behind the upper part of the advisor, which advises the right SW:

The advise is based on the fact that a player needs more force when he has to accelerate the racquet more.

I.O.W.:
Someone who makes his back swing very early can move his racquet backwards slowly because he has a lot of time to do that.
Someone makes his backswing very late (after the bounce) needs much more force to accelerate his racquet because he has less time to bring it around.

So the first player can easily play with a higher SW without needing much force, it will cost the second player a lot of power to play with a high SW.
Compare Söderling with Nadal or even better (for the oldies) with Steffie Graf.

It is logic that stronger and older players can play with higher SW’s easier than tiny built youngsters. That is why you can enter a build and age of the player.

Hi guys,
I think that it might be good to discuss our basic intention:

* I certainly understand that people with knowledge about physics will say that it is impossible to calculate the Swingweight of a racquet very accurately.

But the major question is: Do we want a system that makes it possible to compare racquets or do we need very accurate values of the SW?

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completely agree here. In many, many applications an approximation is good enough. no one argues that. the only point of contention is where you stated in the earlier post:
"This system [e.g. spreadsheet where you enter weights at the ends, and length of the racket] certainly calculates the swing weigth."

it does not do that. it --approximates-- the swingweight, assuming that all rackets have the mass distributed the same way (i.e according to the same function).

If we want to compare racquets we need a “measuring system” , with an accuracy that is as high as possible.

Another fact is that test results from different SW machines differ quite a lot, which proves that this is not an easy measurement to do.
So these machines are impressive and expensive but not accurate.

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Honestly I never heard that before. Do you have a source for that claim?

What is our intentions with the SW advisor?
The idea of the SW came up because we advise the Dutch Tennis Ass about material for young children.
- It should avoid that players play with completely the wrong SW and especially young children.
- We want to make it very easy for coaches to advise the right frame for a certain player.

The system does 3 things:
1. It advises a Swingweight for a certain player based on type of forehand, age and build.

Click to expand...

I can't comment on this. I do not know if there's a biomechanical, medical, or other reason why a given swingweight would be 'the best' for a given player. Perhaps there is. what is the source of that claim?

2. It calculates the SW of a racquet, when head- and throat- weight are entered. (Only have to weigh the weight at both ends of the racquet)
3. When the SW is too low it calculates how much weight should be added at a certain position to get the desired SW.

So for our purpose we need an advise system, a measuring (calculating system) and a way to customize racquets. This is what the Excel sheet (and the online version later) does.

Click to expand...

so it is essentially the same thing that TW's own swingweight calculator does, right?

There are different reasons for this:
* A swing weight test based on measuring the swing time of an object is a very logic choice. The SW can be calculated with one formula from the swing time
T = 6,28 *rt (SW/w*L)

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this is not merely 'a logical choice'. this formula is based on physics laws. You can easily look it up why the formula is the way it is. It is --not-- an approximation, it gives you a swingweight value as per physics definition of what the swingweight actually is.

* Calculating from the Head and throat weight is much more complicated.

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calculating may be (due to the complexity of the formula) - but that is not the point. The point is that 'measuring' the oscillation time is way more complicated that merely measuring the weight. thus overall the method approximating the SW based on weight is way easier (but not exactly accurate).

yes. And these machines provide the functions that the weight-based formula does not. Is it worth thousands of dollars - definitely not to me. I go with Stoneage's app that gives me the exact measurement for $2.00

that video does not show anything that can be used in this discussion. It shows someone weighting a racket and than we see few numbers. I think we can safely assume those SW numbers are --NOT-- an approximation, but the results of actual measurements. if HEAD cannot afford Prince tuning machine i think they can at least get Stoneage's app.....

but again, for what you are doing the approximation is likely quite enough.

It is logic that stronger and older players can play with higher SW’s easier than tiny built youngsters. That is why you can enter a build and age of the player.

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jmnk has given good and relevant replies in his last post so I have nothing to add there.

I just want to say that I have not against you scheme of classifying racquets for different players, it might be useful. But you could skip the swingweight in the scheme. Just use the balance and weight and say that player "so and so" should have a light, top heavy racquet. That is much easier to understand for most players.

Since all racquets with the same weight and balance will get the same swingweight with your formula anyhow it doesn't add anything and it will be easier and clearer just to omit it.